Without Lorentz invariance , spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion \omega \sim k ^ { n } ( n = 2 , 3 , \ldots ) , whose naturalness is protected by polynomial shift symmetries .
Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner ( CHMW ) theorem .
We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes , leading to an evasion of the “ no-go ” consequences of the relativistic CHMW theorem .